The present value of $16,000 discounted back 5 years at an interest rate of 4.5%, compounded semiannually, is approximately $12,867.25, which isn't listed in the provided options, suggesting a need to check for errors in the question.
To calculate the present value of $16,000 discounted back 5 years at an interest rate of 4.5%, compounded semiannually, you use the present value formula:
PV = FV / (1 + r/n)nt
Where:
Plugging in the values, we get:
PV = $16,000 / (1 + 0.045/2)2*5
Now, calculate the denominator:
1 + 0.045/2 = 1.0225
(1.0225)10 = approximately 1.2434
Finally, divide the future value by this number:
PV = $16,000 / 1.2434 ≈ $12,867.25
Therefore, the present value is approximately $12,867.25, which is not listed among the options given, indicating a possible miscalculation or typo in the question, and thus it is advisable to review the interest rate and the compounding frequency. Always double-check the provided options or consult additional resources to ensure accuracy.